Abstrakt:
We conduct global galactic--scale magnetohydrodynamical (MHD) simulations of the cosmic--ray driven dynamo. We assume that exploding stars deposit small--scale, randomly oriented, dipolar magnetic fields into the differentially rotating ISM, together with a portion of cosmic rays, accelerated in supernova shocks. Our simulations are performed with the aid of a new parallel MHD code PIERNIK. We demonstrate that dipolar magnetic fields supplied on small SN--remnant scales, can be amplified exponentially by the CR--driven dynamo to the present equipartition values, and transformed simultaneously to large galactic--scales by an inverse cascade promoted by resistive processes.